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A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force [2005]
- a)dissipates energy as heat
- b)decreases the rotational motion
- c)decreases the rotational and translational motion
- d)converts translational energy to rotational energy
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A drum of radius R and mass M, rolls down without slipping along an in...
Net work done by frictional force when drum rolls down without slipping is zero.
Wnet = 0
Wnet = 0
i.e., converts translation energy to rotational energy.
Most Upvoted Answer
A drum of radius R and mass M, rolls down without slipping along an in...
Let's assume that the inclined plane is inclined at an angle θ with respect to the horizontal. The drum is rolling down the inclined plane without slipping, which means that the linear velocity of the center of mass of the drum is related to its angular velocity by the equation v = Rω, where v is the linear velocity, R is the radius of the drum, and ω is the angular velocity.
The drum is subject to two forces: its weight, mg, acting vertically downwards and the normal force, N, acting perpendicular to the inclined plane. The component of the weight along the inclined plane is mg*sin(θ), which acts to accelerate the drum down the inclined plane. The normal force acts perpendicular to the inclined plane and does not contribute to the acceleration down the inclined plane.
The torque τ about the center of mass of the drum is given by τ = Iα, where I is the moment of inertia of the drum and α is the angular acceleration. Since the drum is rolling without slipping, we have the relationship α = a/R, where a is the linear acceleration down the inclined plane.
The moment of inertia of the drum can be calculated as I = 0.5MR^2, where M is the mass of the drum and R is the radius.
Using Newton's second law for rotation, τ = Iα, we can substitute in the values of I and α, and rearrange the equation to solve for the linear acceleration a:
τ = Iα
mg*sin(θ)*R = 0.5MR^2*a/R
mg*sin(θ) = 0.5Ma
a = 2*g*sin(θ)
Therefore, the linear acceleration of the drum down the inclined plane is given by a = 2*g*sin(θ), where g is the acceleration due to gravity.
Note that this result is independent of the radius of the drum. The only factors that affect the acceleration are the mass of the drum, the angle of the inclined plane, and the acceleration due to gravity.
The drum is subject to two forces: its weight, mg, acting vertically downwards and the normal force, N, acting perpendicular to the inclined plane. The component of the weight along the inclined plane is mg*sin(θ), which acts to accelerate the drum down the inclined plane. The normal force acts perpendicular to the inclined plane and does not contribute to the acceleration down the inclined plane.
The torque τ about the center of mass of the drum is given by τ = Iα, where I is the moment of inertia of the drum and α is the angular acceleration. Since the drum is rolling without slipping, we have the relationship α = a/R, where a is the linear acceleration down the inclined plane.
The moment of inertia of the drum can be calculated as I = 0.5MR^2, where M is the mass of the drum and R is the radius.
Using Newton's second law for rotation, τ = Iα, we can substitute in the values of I and α, and rearrange the equation to solve for the linear acceleration a:
τ = Iα
mg*sin(θ)*R = 0.5MR^2*a/R
mg*sin(θ) = 0.5Ma
a = 2*g*sin(θ)
Therefore, the linear acceleration of the drum down the inclined plane is given by a = 2*g*sin(θ), where g is the acceleration due to gravity.
Note that this result is independent of the radius of the drum. The only factors that affect the acceleration are the mass of the drum, the angle of the inclined plane, and the acceleration due to gravity.
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A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force [2005]a)dissipates energy as heatb)decreases the rotational motionc)decreases the rotational and translational motiond)converts translational energy to rotational energyCorrect answer is option 'D'. Can you explain this answer?
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A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force [2005]a)dissipates energy as heatb)decreases the rotational motionc)decreases the rotational and translational motiond)converts translational energy to rotational energyCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force [2005]a)dissipates energy as heatb)decreases the rotational motionc)decreases the rotational and translational motiond)converts translational energy to rotational energyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force [2005]a)dissipates energy as heatb)decreases the rotational motionc)decreases the rotational and translational motiond)converts translational energy to rotational energyCorrect answer is option 'D'. Can you explain this answer?.
A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force [2005]a)dissipates energy as heatb)decreases the rotational motionc)decreases the rotational and translational motiond)converts translational energy to rotational energyCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force [2005]a)dissipates energy as heatb)decreases the rotational motionc)decreases the rotational and translational motiond)converts translational energy to rotational energyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force [2005]a)dissipates energy as heatb)decreases the rotational motionc)decreases the rotational and translational motiond)converts translational energy to rotational energyCorrect answer is option 'D'. Can you explain this answer?.
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